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Generalized Continuum Mechanics And Engineering Applications

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Generalized Continuum Mechanics and Engineering Applications

Generalized Continuum Mechanics and Engineering Applications Book
Author : Angela Madeo
Publisher : Elsevier
Release : 2015-10-31
ISBN : 0081004672
Language : En, Es, Fr & De

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Book Description :

The new concept of metamaterial is increasingly attracting the interest of physicists and mechanical engineers. Such materials are obtained by suitably assembling multiple individual elements but usually arranged in (quasi-)periodic substructures in order to show exotic global mechanical properties. Indeed, the particular shape, geometry, size, orientation and arrangement of their constituting elements can affect, the propagation of waves of light or sound in a manner not observed in natural materials, creating material properties which may give rise to unexpected engineering applications. Particularly promising in the design and description of metamaterials are those micro-structures which present high contrasts in their mechanical properties: these micro-structures, once homogenized, may produce generalized continuum media, for example, second gradient or micromorphic. Many scientific challenges related to the application of generalized continuum theories to the characterization and conception of high-performance metamaterials can be identified. In this book we identify and discuss four main potential fields of applications of generalized continuum theories, namely, mechanical behavior of fibrous composite reinforcements, wave propagation in metamaterials, mechanical behavior of concrete and mechanically driven remodeling of bone in presence of bio-resorbable materials. For each field, we underline how the use of a generalized continuum theory can be of help for describing how the presence of microstructure can affect the global mechanical behavior of the considered metamaterials. Covers four main fields of the application of continuum theories Learn how to apply generalised continuum theory to describe the effects of microstructure on the mechanical behavior of materials Decipher the material properties which aid your engineering applications

Generalized Continua from the Theory to Engineering Applications

Generalized Continua   from the Theory to Engineering Applications Book
Author : Holm Altenbach,Victor A. Eremeyev
Publisher : Springer Science & Business Media
Release : 2012-10-17
ISBN : 3709113717
Language : En, Es, Fr & De

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Book Description :

On the roots of continuum mechanics in differential geometry -- a review.- Cosserat media.- Cosserat-type shells.- Cosserat-type rods.- Micromorphic media.- Electromagnetism and generalized continua.- Computational methods for generalized continua. The need of generalized continua models is coming from practice. Complex material behavior sometimes cannot be presented by the classical Cauchy continua. At present the attention of the scientists in this field is focused on the most recent research items • new models, • application of well-known models to new problems, • micro-macro aspects, • computational effort, and • possibilities to identify the constitutive equations The new research directions are discussed in this volume - from the point of view of modeling and simulation, identification, and numerical methods.

Applications Of Tensor Analysis In Continuum Mechanics

Applications Of Tensor Analysis In Continuum Mechanics Book
Author : Michael J Cloud,Victor A Eremeyev,Leonid P Lebedev
Publisher : World Scientific
Release : 2018-07-10
ISBN : 9813238984
Language : En, Es, Fr & De

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Book Description :

'A strong point of this book is its coverage of tensor theory, which is herein deemed both more readable and more substantial than many other historic continuum mechanics books. The book is self-contained. It serves admirably as a reference resource on fundamental principles and equations of tensor mathematics applied to continuum mechanics. Exercises and problem sets are useful for teaching … The book is highly recommended as both a graduate textbook and a reference work for students and more senior researchers involved in theoretical and mathematical modelling of continuum mechanics of materials. Key concepts are well described in the text and are supplemented by informative exercises and problem sets with solutions, and comprehensive Appendices provide important equations for ease of reference.'Contemporary PhysicsA tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions.This book provides a clear, concise, and self-contained treatment of tensors and tensor fields. It covers the foundations of linear elasticity, shell theory, and generalized continuum media, offers hints, answers, and full solutions for many of the problems and exercises, and Includes a handbook-style summary of important tensor formulas.The book can be useful for beginners who are interested in the basics of tensor calculus. It also can be used by experienced readers who seek a comprehensive review on applications of the tensor calculus in mechanics.

Variational Principles of Continuum Mechanics with Engineering Applications

Variational Principles of Continuum Mechanics with Engineering Applications Book
Author : V. Komkov
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 9400945647
Language : En, Es, Fr & De

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Book Description :

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Geometrical Foundations of Continuum Mechanics

Geometrical Foundations of Continuum Mechanics Book
Author : Paul Steinmann
Publisher : Springer
Release : 2015-03-25
ISBN : 3662464608
Language : En, Es, Fr & De

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Book Description :

This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity. After a motivation that arises from considering geometrically linear first- and second- order crystal plasticity in Part I several concepts from differential geometry, relevant for what follows, such as connection, parallel transport, torsion, curvature, and metric for holonomic and anholonomic coordinate transformations are reiterated in Part II. Then, in Part III, the kinematics of geometrically nonlinear continuum mechanics are considered. There various concepts of differential geometry, in particular aspects related to compatibility, are generically applied to the kinematics of first- and second- order geometrically nonlinear continuum mechanics. Together with the discussion on the integrability conditions for the distortions and double-distortions, the concepts of dislocation, disclination and point-defect density tensors are introduced. For concreteness, after touching on nonlinear fir st- and second-order elasticity, a detailed discussion of the kinematics of (multiplicative) first- and second-order elasto-plasticity is given. The discussion naturally culminates in a comprehensive set of different types of dislocation, disclination and point-defect density tensors. It is argued, that these can potentially be used to model densities of geometrically necessary defects and the accompanying hardening in crystalline materials. Eventually Part IV summarizes the above findings on integrability whereby distinction is made between the straightforward conditions for the distortion and the double-distortion being integrable and the more involved conditions for the strain (metric) and the double-strain (connection) being integrable. The book addresses readers with an interest in continuum modelling of solids from engineering and the sciences alike, whereby a sound knowledge of tensor calculus and continuum mechanics is required as a prerequisite.

Mechanics of Generalized Continua

Mechanics of Generalized Continua Book
Author : Gérard A. Maugin,Andrei V. Metrikine
Publisher : Springer Science & Business Media
Release : 2010-03-24
ISBN : 1441956956
Language : En, Es, Fr & De

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Book Description :

In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.

Generalized Continua from the Theory to Engineering Applications

Generalized Continua   from the Theory to Engineering Applications Book
Author : Holm Altenbach,Victor A. Eremeyev
Publisher : Springer Science & Business Media
Release : 2012-10-18
ISBN : 3709113709
Language : En, Es, Fr & De

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Book Description :

On the roots of continuum mechanics in differential geometry -- a review.- Cosserat media.- Cosserat-type shells.- Cosserat-type rods.- Micromorphic media.- Electromagnetism and generalized continua.- Computational methods for generalized continua. The need of generalized continua models is coming from practice. Complex material behavior sometimes cannot be presented by the classical Cauchy continua. At present the attention of the scientists in this field is focused on the most recent research items • new models, • application of well-known models to new problems, • micro-macro aspects, • computational effort, and • possibilities to identify the constitutive equations The new research directions are discussed in this volume - from the point of view of modeling and simulation, identification, and numerical methods.

Higher Gradient Materials and Related Generalized Continua

Higher Gradient Materials and Related Generalized Continua Book
Author : Holm Altenbach,Wolfgang H. Müller,Bilen Emek Abali
Publisher : Springer Nature
Release : 2019-11-04
ISBN : 303030406X
Language : En, Es, Fr & De

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Book Description :

This book discusses recent findings and advanced theories presented at two workshops at TU Berlin in 2017 and 2018. It underlines several advantages of generalized continuum models compared to the classical Cauchy continuum, which although widely used in engineering practice, has a number of limitations, such as: • The structural size is very small. • The microstructure is complex. • The effects are localized. As such, the development of generalized continuum models is helpful and results in a better description of the behavior of structures or materials. At the same time, there are more and more experimental studies supporting the new models because the number of material parameters is higher.

Continuum Mechanics Through the Eighteenth and Nineteenth Centuries

Continuum Mechanics Through the Eighteenth and Nineteenth Centuries Book
Author : Gérard A. Maugin
Publisher : Springer Science & Business Media
Release : 2014-04-04
ISBN : 3319053744
Language : En, Es, Fr & De

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Book Description :

Conceived as a series of more or less autonomous essays, the present book critically exposes the initial developments of continuum thermo-mechanics in a post Newtonian period extending from the creative works of the Bernoullis to the First World war, i.e., roughly during first the “Age of reason” and next the “Birth of the modern world”. The emphasis is rightly placed on the original contributions from the “Continental” scientists (the Bernoulli family, Euler, d’Alembert, Lagrange, Cauchy, Piola, Duhamel, Neumann, Clebsch, Kirchhoff, Helmholtz, Saint-Venant, Boussinesq, the Cosserat brothers, Caratheodory) in competition with their British peers (Green, Kelvin, Stokes, Maxwell, Rayleigh, Love,..). It underlines the main breakthroughs as well as the secondary ones. It highlights the role of scientists who left essential prints in this history of scientific ideas. The book shows how the formidable developments that blossomed in the twentieth century (and perused in a previous book of the author in the same Springer Series: “Continuum Mechanics through the Twentieth Century”, Springer 2013) found rich compost in the constructive foundational achievements of the eighteenth and nineteenth centuries. The pre-WWI situation is well summarized by a thorough analysis of treatises (Appell, Hellinger) published at that time. English translations by the author of most critical texts in French or German are given to the benefit of the readers.

Advances in Mechanics of Microstructured Media and Structures

Advances in Mechanics of Microstructured Media and Structures Book
Author : Francesco dell'Isola,Victor A. Eremeyev,Alexey Porubov
Publisher : Springer
Release : 2018-03-28
ISBN : 3319736949
Language : En, Es, Fr & De

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Book Description :

This book is an homage to the pioneering works of E. Aero and G. Maugin in the area of analytical description of generalized continua. It presents a collection of contributions on micropolar, micromorphic and strain gradient media, media with internal variables, metamaterials, beam lattices, liquid crystals, and others. The main focus is on wave propagation, stability problems, homogenization, and relations between discrete and continuous models.

Generalized Models and Non classical Approaches in Complex Materials 1

Generalized Models and Non classical Approaches in Complex Materials 1 Book
Author : Holm Altenbach,Joël Pouget,Martine Rousseau,Bernard Collet,Thomas Michelitsch
Publisher : Springer
Release : 2018-03-24
ISBN : 3319724401
Language : En, Es, Fr & De

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Book Description :

This book is the first of 2 special volumes dedicated to the memory of Gérard Maugin. Including 40 papers that reflect his vast field of scientific activity, the contributions discuss non-standard methods (generalized model) to demonstrate the wide range of subjects that were covered by this exceptional scientific leader. The topics range from micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro–macro aspects, computational endeavors, options for identifying constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.

Continuum Mechanics through the Ages From the Renaissance to the Twentieth Century

Continuum Mechanics through the Ages   From the Renaissance to the Twentieth Century Book
Author : Gérard A. Maugin
Publisher : Springer
Release : 2015-11-19
ISBN : 3319265938
Language : En, Es, Fr & De

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Book Description :

Mixing scientific, historic and socio-economic vision, this unique book complements two previously published volumes on the history of continuum mechanics from this distinguished author. In this volume, Gérard A. Maugin looks at the period from the renaissance to the twentieth century and he includes an appraisal of the ever enduring competition between molecular and continuum modelling views. Chapters trace early works in hydraulics and fluid mechanics not covered in the other volumes and the author investigates experimental approaches, essentially before the introduction of a true concept of stress tensor. The treatment of such topics as the viscoelasticity of solids and plasticity, fracture theory, and the role of geometry as a cornerstone of the field, are all explored. Readers will find a kind of socio-historical appraisal of the seminal contributions by our direct masters in the second half of the twentieth century. The analysis of the teaching and research texts by Duhem, Poincaré and Hilbert on continuum mechanics is key: these provide the most valuable documentary basis on which a revival of continuum mechanics and its formalization were offered in the late twentieth century. Altogether, the three volumes offer a generous conspectus of the developments of continuum mechanics between the sixteenth century and the dawn of the twenty-first century. Mechanical engineers, applied mathematicians and physicists alike will all be interested in this work which appeals to all curious scientists for whom continuum mechanics as a vividly evolving science still has its own mysteries.

Non Classical Continuum Mechanics

Non Classical Continuum Mechanics Book
Author : Gérard A. Maugin
Publisher : Springer
Release : 2016-09-24
ISBN : 9811024340
Language : En, Es, Fr & De

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Book Description :

This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, ever y entry is followed by a cross-reference to other related subject entries in the dictionary.

Mechanics of Generalized Continua

Mechanics of Generalized Continua Book
Author : Holm Altenbach,Gérard A. Maugin,Vladimir Erofeev
Publisher : Springer Science & Business Media
Release : 2011-04-02
ISBN : 9783642192197
Language : En, Es, Fr & De

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Book Description :

This collection on „Mechanics of Generalized Continua - from Micromechanical Basics to Engineering Applications“ brings together leading scientists in this field from France, Russian Federation, and Germany. The attention in this publication is be focussed on the most recent research items, i.e., - new models, - application of well-known models to new problems, - micro-macro aspects, - computational effort, - possibilities to identify the constitutive equations, and - old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.

Size Dependent Continuum Mechanics Approaches

Size Dependent Continuum Mechanics Approaches Book
Author : Esmaeal Ghavanloo
Publisher : Springer Nature
Release : 2021-09-26
ISBN : 3030630501
Language : En, Es, Fr & De

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Book Description :

Download Size Dependent Continuum Mechanics Approaches book written by Esmaeal Ghavanloo, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Continuum Mechanics Through the Twentieth Century

Continuum Mechanics Through the Twentieth Century Book
Author : Gerard A Maugin
Publisher : Springer Science & Business Media
Release : 2013-04-08
ISBN : 9400763530
Language : En, Es, Fr & De

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Book Description :

This overview of the development of continuum mechanics throughout the twentieth century is unique and ambitious. Utilizing a historical perspective, it combines an exposition on the technical progress made in the field and a marked interest in the role played by remarkable individuals and scientific schools and institutions on a rapidly evolving social background. It underlines the newly raised technical questions and their answers, and the ongoing reflections on the bases of continuum mechanics associated, or in competition, with other branches of the physical sciences, including thermodynamics. The emphasis is placed on the development of a more realistic modeling of deformable solids and the exploitation of new mathematical tools. The book presents a balanced appraisal of advances made in various parts of the world. The author contributes his technical expertise, personal recollections, and international experience to this general overview, which is very informative albeit concise.

New Achievements in Continuum Mechanics and Thermodynamics

New Achievements in Continuum Mechanics and Thermodynamics Book
Author : Bilen Emek Abali,Holm Altenbach,Francesco dell'Isola,Victor A. Eremeyev,Andreas Öchsner
Publisher : Springer
Release : 2019-03-13
ISBN : 3030133079
Language : En, Es, Fr & De

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Book Description :

This book presents a liber amicorum dedicated to Wolfgang H. Müller, and highlights recent advances in Prof. Müller’s major fields of research: continuum mechanics, generalized mechanics, thermodynamics, mechanochemistry, and geomechanics. Over 50 of Prof. Müller’s friends and colleagues contributed to this book, which commemorates his 60th birthday and was published in recognition of his outstanding contributions.

Continuum Mechanics

Continuum Mechanics Book
Author : Yong Gan
Publisher : BoD – Books on Demand
Release : 2012-03-28
ISBN : 9535104470
Language : En, Es, Fr & De

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Book Description :

Continuum Mechanics is the foundation for Applied Mechanics. There are numerous books on Continuum Mechanics with the main focus on the macroscale mechanical behavior of materials. Unlike classical Continuum Mechanics books, this book summarizes the advances of Continuum Mechanics in several defined areas. Emphasis is placed on the application aspect. The applications described in the book cover energy materials and systems (fuel cell materials and electrodes), materials removal, and mechanical response/deformation of structural components including plates, pipelines etc. Researchers from different fields should be benefited from reading the mechanics approached to real engineering problems.

Generalized Models and Non classical Approaches in Complex Materials 2

Generalized Models and Non classical Approaches in Complex Materials 2 Book
Author : Holm Altenbach,Joël Pouget,Martine Rousseau,Bernard Collet,Thomas Michelitsch
Publisher : Springer
Release : 2018-06-26
ISBN : 3319775049
Language : En, Es, Fr & De

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Book Description :

This book is the 2nd special volume dedicated to the memory of Gérard Maugin. Over 30 leading scientists present their contribution to reflect the vast field of scientific activity of Gérard Maugin. The topics of contributions employing often non-standard methods (generalized model) in this volume show the wide range of subjects that were covered by this exceptional scientific leader. The topics range from micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro-macro aspects, computational efforts, possibilities to identify the constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.

Continuum Mechanics with Eulerian Formulations of Constitutive Equations

Continuum Mechanics with Eulerian Formulations of Constitutive Equations Book
Author : M.B. Rubin
Publisher : Springer Nature
Release : 2020-10-11
ISBN : 3030577767
Language : En, Es, Fr & De

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Book Description :

This book focuses on the need for an Eulerian formulation of constitutive equations. After introducing tensor analysis using both index and direct notation, nonlinear kinematics of continua is presented. The balance laws of the purely mechanical theory are discussed along with restrictions on constitutive equations due to superposed rigid body motion. The balance laws of the thermomechanical theory are discussed and specific constitutive equations are presented for: hyperelastic materials; elastic–inelastic materials; thermoelastic–inelastic materials with application to shock waves; thermoelastic–inelastic porous materials; and thermoelastic–inelastic growing biological tissues.